Question

Expand (1/3x -2/3y)^3

Answer 1

(a-b)(a^2 + b^2 +ab)
(1/3x-2/3y)(1/9x^2 + 4/9y^2 + 2/9xy)

Answer 2

Given,

It is given that (1/3x - 2/3y)³.

To find,

We have to expand the expression (1/3x - 2/3y)³.

Solution,

The expanded form of  (1/3x - 2/3y)³ is (x³-8y³-6x²y+12xy²)/27.

We can simply find the expanded form of the given cubic expression by using the algebraic identity,

    (a-b)³ = a³ -b³ -3ab(a-b)

a = 1/3x , b = 2/3y

Using the above identity, we get

(1/3x)³ - (2/3y)³ -3(1/3x)(2/3y) [1/3x-2/3y]

1/27x³ - 8/27y³ -2/9x²y+4/9xy²

Taking the LCM, we get

(x³ - 8y³ -6x²y + 12xy²)/27

Hence, the expanded form of (1/3x - 2/3y)³ is (x³ - 8y³ -6x²y + 12xy²)/27.